Publication list

Link to all publications

Books

  1. W. Górny and J.M. Mazón, Functions of Least Gradient, Monographs in Mathematics, vol. 110, 2024, ISBN 978-3-031-51880-5. DOI: 10.1007/978-3-031-51881-2.
  2. W. Górny and J.M. Mazón, Weak Solutions to Gradient Flows in Metric Measure Spaces, accepted for publication in the Cambridge University Press series “Cambridge Tracts in Mathematics”, to appear in 2026.

Journal articles

  1. W. Górny, P. Rybka and A. Sabra, Special cases of the planar least gradient problem, Nonlinear Anal. 151 (2017), pp. 66-95. DOI: 10.1016/j.na.2016.11.020.
  2. W. Górny, Planar least gradient problem: existence, regularity and anisotropic case, Calc. Var. Partial Differential Equations 57, no. 4 (2018), Art. 98. DOI: 10.1007/s00526-018-1378-y.
  3. W. Górny, (Non)uniqueness of minimizers in the least gradient problem, J. Math. Anal. Appl. 468 (2018), pp. 913-938. DOI: 10.1016/j.jmaa.2018.08.038.
  4. W. Górny, Lp regularity of least gradient functions, Proc. Amer. Math. Soc. 148 (7) (2020), pp. 3009-3019. DOI: 10.1090/proc/15031.
  5. W. Górny, Least gradient problem with respect to a non-strictly convex norm, Nonlinear Anal. 200 (2020), 112049. DOI: 10.1016/j.na.2020.112049.
  6. W. Górny and J.M. Mazón, Least gradient functions in metric random walk spaces, ESAIM:COCV 27 (2021), S28. DOI: 10.1051/cocv/2020087.
  7. W. Górny, Existence of minimisers in the least gradient problem for general boundary data, Indiana Univ. Math. J. 70, no. 3 (2021), pp. 1003-1037. DOI: 10.1512/iumj.2021.70.8420.
  8. W. Górny, Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents, J. Geom. Anal. 32 (4) (2022), Art. 128. DOI: 10.1007/s12220-021-00861-4.
  9. W. Górny, Local and nonlocal 1-Laplacian in Carnot groups, Ann. Fenn. Math. 47 (1) (2022), pp. 427-456. DOI: 10.54330/afm.114742.
  10. S. Dweik and W. Górny, Least gradient problem on annuli, Analysis & PDE 15 (3) (2022), pp. 699-725. DOI: 10.2140/apde.2022.15.699.
  11. W. Górny and J.M. Mazón, On the p-Laplacian evolution equation in metric measure spaces, J. Funct. Anal. 283 (2022), 109621. DOI: 10.1016/j.jfa.2022.109621.
  12. W. Górny, The trace space of anisotropic least gradient functions depends on the anisotropy, Math. Ann. 387 (2023), 1343–1365. DOI: 10.1007/s00208-022-02488-4.
  13. S. Dweik and W. Górny, Optimal transport approach to Sobolev regularity of solutions to the weighted least gradient problem, SIAM. J. Math. Anal. 55 (2023), no. 3, pp. 1916-1948. DOI: 10.1137/21M1468358.
  14. W. Górny, Applications of optimal transport methods in the least gradient problem, Ann. Scu. Norm. Sup. Pisa Cl. Sci. (5) 24 (2023), pp. 1817-1851. DOI: 10.2422/2036-2145.202105_049.
  15. W. Górny and J.M. Mazón, The Neumann and Dirichlet problems for the total variation flow in metric measure spaces, Adv. Calc. Var. 17 (2024), 131-164. DOI: 10.1515/acv-2021-0107.
  16. W. Górny and J.M. Mazón, The Anzellotti-Gauss-Green formula and least gradient functions in metric measure spaces, Commun. Contemp. Math. 26 (2024), no. 6, 2350027. DOI: 10.1142/S021919972350027X.
  17. M. Friedrich, W. Górny and U. Stefanelli, The double-bubble problem on the square lattice, Interfaces Free Bound. 26 (2024), no. 1, pp. 79-134. DOI: 10.4171/ifb/510.
  18. W. Górny, Least gradient problem with Dirichlet condition imposed on a part of the boundary, Calc. Var. Partial Differential Equations 63 (2024), Art. 58. DOI: 10.1007/s00526-023-02646-9.
  19. M. Friedrich, W. Górny and U. Stefanelli, A characterization of l1 double bubbles with general interface interaction, Adv. Calc. Var. 18 (2025), 609-637. DOI: 10.1515/acv-2023-0131.
  20. W. Górny, Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces, J. Evol. Equ. 25 (2025), Art. 44. DOI: 10.1007/s00028-025-01071-z.
  21. W. Górny, J.M. Mazón, J. Toledo, Evolution problems with perturbed 1-Laplacian type operators on random walk spaces, Math. Ann. 392 (2025), 3895-3957. DOI: 10.1007/s00208-025-03180-z.
  22. W. Górny, Strongly anisotropic Anzellotti pairings and their applications to the anisotropic p-Laplacian, J. Math. Anal. Appl. 552 (2025), 129734. DOI: 10.1016/j.jmaa.2025.129734.
  23. W. Górny and J.M. Mazón, A duality-based approach to gradient flows of linear growth functionals, Publ. Mat. 69 (2025), 341-365. DOI: 10.5565/PUBLMAT6922504.
  24. M. Friedrich, W. Górny and U. Stefanelli, The l1 double-bubble problem in three dimensions, J. Geom. Anal. 35 (2025), Art. 323. DOI: 10.1007/s12220-025-02151-9.
  25. W. Górny, M. Łasica, A. Matsoukas, Euler–Lagrange equations for variable-growth total variation, Nonlinear Anal. 263 (2026), 113984. DOI: 10.1016/j.na.2025.113984.
  26. S. Buccheri and W. Górny, A metric counterpart of the Gu-Yung formula, Rev. Mat. Complut., to appear, preprint available at arXiv:2403.13475.

Conference proceedings

  1. W. Górny and J.M. Mazón, Weak solutions to gradient flows in metric measure spaces, Proc. Appl. Math. Mech. 22:1 (2022), e202200099. DOI: 10.1002/pamm.202200099.
  2. W. Górny and J.M. Mazón, Weak solutions to the total variation flow in metric measure spaces, in: Ferreira et al. (eds.), Proceedings book. XXVII Congreso de Ecuaciones Diferenciales y XVII Congreso de Matemática Aplicada, Zaragoza, July 18th–22nd, 2022. Prensas de la Universidad de Zaragoza, pp. 55--62, 2023. DOI: 10.26754/uz.978-84-18321-66-5.

Preprints

  1. W. Górny, M. Łasica, A. Matsoukas, Adaptive double-phase Rudin–Osher–Fatemi denoising model, preprint (2025), available at arXiv:2510.04382.